Question: Solve for $x$ and $y$ using elimination. ${3x+6y = 60}$ ${-3x-5y = -51}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $3x$ and $-3x$ cancel out. ${y = 9}$ Now that you know ${y = 9}$ , plug it back into $\thinspace {3x+6y = 60}\thinspace$ to find $x$ ${3x + 6}{(9)}{= 60}$ $3x+54 = 60$ $3x+54{-54} = 60{-54}$ $3x = 6$ $\dfrac{3x}{{3}} = \dfrac{6}{{3}}$ ${x = 2}$ You can also plug ${y = 9}$ into $\thinspace {-3x-5y = -51}\thinspace$ and get the same answer for $x$ : ${-3x - 5}{(9)}{= -51}$ ${x = 2}$